The British actor said that playing Owen Harper in spinoff Torchwood has "closed the door" for a potential appointment as the Time Lord.
Speaking to Jon Hornbuckle for Digital Spy, Gorman said: "I'm afraid the Doctor Who door is probably closed because of me being in Torchwood.
"I'm really excited to see who it will be, let's hope they go with someone different but I'm sure whoever they choose will be amazing."
Matt Smith will stand down as the Doctor after this year's Christmas special. Many actors including Gorman have been tipped for his replacement.
Ben Daniels, Helen Mirren, Julian Rhind-Tutt and Dominic Cooper are among the names linked with the role in recent weeks.
Gorman also spoke about the passion of Torchwood fans, saying: "I'm a fan myself so I understand where [the obsession] comes from and in terms of the whole Doctor Who/Torchwood fandom.
"They are the most educated fans in the world and I've seriously never had anything but great feedback. I had a great time doing Torchwood, I really did."
Burn Gorman stars as Dr Hermann Gottlieb in the Guillermo del Toro movie Pacific Rim, which will open in 3D, IMAX 3D and 2D cinemas on July 12.
Watch a trailer for Pacific Rim below: